A crate has a mass of 27 kg. What applied force is required to produce an acceleration of 3 m/s2 if the frictional force is known to be 98 N?
I am confused on how to solve this.
ma=F-F(fr),
F= ma+F(fr)
To solve this problem, you can use Newton's second law of motion, which states that the applied force (F) is equal to the mass (m) of an object multiplied by its acceleration (a). Mathematically, it can be written as F = m * a.
In this particular problem, you are given the mass of the crate (27 kg) and the desired acceleration (3 m/s^2).
1. Write down the values you know:
Mass (m) = 27 kg
Acceleration (a) = 3 m/s^2
2. Use Newton's second law to find the applied force (F):
F = m * a
F = 27 kg * 3 m/s^2
F = 81 kg⋅m/s^2
3. Recall that force is measured in Newtons (N), not kg⋅m/s^2. To convert it, you need to use the relationship F = ma, where a represents acceleration due to gravity. On Earth, acceleration due to gravity is approximately 9.8 m/s^2.
4. Subtract the force of friction (98 N) from the calculated force to find the applied force:
Applied force = Calculated force − Frictional force
Applied force = 81 N − 98 N
Applied force = -17 N
The negative sign indicates that the applied force is in the opposite direction of motion, which suggests that the applied force is not enough to overcome the frictional force.